An 800-Year-Old Mathematical Trick May Be the Key to Lunar Navigation
We’ve been landing people on the Moon since 1969, but how will astronauts find their way around once lunar exploration begins? The moon needs a Global Navigation Satellite System (GNSS), and an 800-year-old mathematical trick might help.
The mathematical trick in question is known as the Fibonacci sphere. Here, researchers at Hungary’s Eötvös Loránd University used the Fibonacci sphere to more accurately estimate the moon’s spinning ellipsoid, a shape that is slightly squashed as it orbits the earth.
Due to the effects of gravity, rotation, and tidal fluctuations, the Earth and Moon are shaped like a squashed ball.
For simplicity, our GNSS technology uses a rough estimate of the Earth’s squashed ball shape. If we are to develop a geographic information system (GIS) for the Moon, we need the same estimation for the Moon’s selenoid (the true irregular shape, equivalent to the Earth’s geoid).
Geophysicist Gábor Timár and student Kamilla Cziráki write in their published paper, “Most lunar GIS applications use spherical datums because the Moon is less flat than the Earth. But with the renaissance of lunar exploration, it seems worthwhile to define a rotating ellipsoid that better fits the selenoid.”
This brings us back to the Fibonacci sphere, which uses an approach based on the Fibonacci sequence to evenly distribute points on a sphere; Cziráki and Timár mapped 100,000 points on the Moon previously measured by NASA using a computational model based on the Fibonacci sphere.
The results provided more accurate values for the semi-major and semi-minor axes that define the lunar rotational ellipsoid. Since the lunar poles are about half a kilometer (0.3 miles) closer to the center of the Moon than the equator, incorporating this information into future lunar GPS would reduce misorientation on the Moon.
Calculations of this level of detail have not been done on the Moon since the 1960s. Furthermore, when researchers applied this technique to the Earth’s rotating ellipsoid, the data matched up beautifully. The results of this study will not only help provide a better navigation system for people heading to the Moon in the future, but could also be used to estimate the size of the Earth and improve navigation systems for orbiting the Earth.
In the future,” the researchers write, “we would like to extend this research to the Earth and investigate the differences between the best-fitting ellipsoids using various geoid models.
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